Cosmic Theories - Kepler and Newton

Kepler and his Laws

Johannes Kepler (1571-1630) spent a great deal of time trying to understand the physics of the cosmos. After Copernicus and Tycho he was able to think in terms of the planets moving free of celestial spheres around the Sun. Using the motions of Mars and detailed observations from Tycho, he eventually devised his three laws of orbital motion:

  • A planet's orbit is an ellipse with the Sun at one focus.

  • A line from the Sun to the planet traces out equal areas in equal times.

  • The square of a planets period is in a fixed ratio to the cube of the average radius of its orbit.

Kepler realised that Copernicus's Sun-centred cosmos must be real, but debate continued to rage until Newton eventually confirmed that Kepler's theory was consistent with his newly-formed theory of Gravity.

  • The diagram shows an ellipse with exaggerated eccentricity. Planetary orbits are much closer to circles.

a is the semi-major axis, b is the semi-minor axis of the ellipse. The Sun is at one focus, the other focus is empty. The degree to which a is greater than b is the 'eccentricity' of the orbit. You can see that the planet moves more slowly when it is farther away from the Sun so that the area swept by the Sun-planet line remains constant per unit of time.

Newton's Laws

Isaac Newton (1643 - 1727) developed the first fundamental 'laws' of mechanics.  It is worth reminding ourselves of these laws:

  • A body remains at rest, or moves in a straight line at a constant speed, unless acted upon by an outside force.

  • Acceleration (change of speed/direction) of a body is proportional to the outside force acting on it.

  • When one body exerts a force on a second body then the second body exerts an equal and opposite force on the first body.

  • Two bodies attract each other with a force (gravity) that is directly proportional to the mass of each body and inversely proportional to the square of the distance between them.

Newton provided a mathematical proof showing that, if these laws are true, Kepler's laws are also true. At last it was possible to explain and predict the motions of the Sun, Moon and planets based on a theory that involved natural physical objects and resonable "laws" of motion.

At this point in the story we may say that 'ancient cosmologies' gave way to modern science. For an interactive demonstration of the consequence of Newton's laws, go to the Orbit Simulation area of the website.

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Tony Evans 2004-2011

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